Dynamo action due to turbulence in a linear shear flow

Abstract

Astrophysical systems such as the Sun, disc galaxies, galaxy clusters, and accretion discs possess ordered magnetic fields alongside random components. These magnetic fields survive for timescales much longer than diffusion times, suggesting they are self-sustained by turbulent dynamo action. Dynamo action converts kinetic energy into magnetic energy without external currents at infinity.

The standard paradigm involves amplification of seed magnetic fields via helical turbulent flows (the -effect). However, recent studies show that mean shear flows can also break mirror symmetry and drive large-scale dynamo action, even in the absence of net helicity. This motivates the study of the shear dynamo problem without the usual -effect.

Problems Studied 1. Shearing Waves

Shear flows are common in astrophysical contexts (e.g., disc galaxies, accretion discs).

Random stirring events (e.g., supernovae) excite shearing waves in these systems.

Exact solutions of the incompressible Navier-Stokes equations in background linear shear flow were obtained, with time-dependent wave vectors.

Forced stochastic velocity dynamics was studied at low Reynolds numbers, modeling non-helical turbulence in shear flows.

These results provide insight into transport coefficients relevant for dynamo action.

2. Passive Scalar Mixing in Shear Flows

Passive scalars evolve via the advection-diffusion equation, offering a simpler test case than magnetic fields.

Using non-helical stochastic shearing wave solutions, the mixing of passive scalars was analyzed.

The key question addressed: under what conditions does the mean concentration of a passive scalar grow due to mirror-symmetric turbulence in shear flows

3. The Shear Dynamo Problem

In a background shear flow, non-helical stirring of conducting fluid can lead to growth of large-scale magnetic fields.

This represents an inverse cascade, transferring energy from small to large scales.

Numerical simulations (using the Pencil Code) in unexplored parameter regimes confirmed dynamo action without net -effect.

Analytical studies showed that fluctuations in with zero mean, combined with background shear, can drive large-scale dynamo action.

This aligns with earlier arguments (Kraichnan, 1976) that helicity fluctuations can sustain dynamo growth.